Throughout, we assume that processes \(\eta \)  and \(L\)  are
additive processes.
An additive process \(V:=(V(u))_{u\ge 0}\)  has independent
increments with càdlàg path starting at \(V(0)=0\)  a.s.
and is stochastically continuous.
The distribution of the process \(V\)  is completely determined by the system of generating triplet
\(\lbrace (A_u,\rho _u,\gamma _u):u\ge 0\rbrace \)  via characteristic function. See
[1]} for more details. We will restrict ourselves to processes
having only a pure jump part (see [1]}), namely
we consider \(V\)  such that
\(E[ e^{ix V(u)}]=\exp \Big \lbrace \int _{(0,u]\times \mathbb {R}} (e^{ixv}-1)\, \rho (d (w,v))\Big \rbrace ,\) 
